Module stripy.cartesian_meshes

Copyright 2017-2019 Louis Moresi, Ben Mather

This file is part of Stripy.

Stripy is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version.

Stripy is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with Stripy. If not, see http://www.gnu.org/licenses/.

"""
Copyright 2017-2019 Louis Moresi, Ben Mather

This file is part of Stripy.

Stripy is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or any later version.

Stripy is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License
along with Stripy.  If not, see <http://www.gnu.org/licenses/>.
"""

#!/usr/bin/python
# -*- coding: utf-8 -*-
from . import cartesian as _cartesian
import numpy as np


class square_border(_cartesian.Triangulation):
    """
    Square border to add to any mesh.
    Creates a set of points around the extent of the domain.
    """
    def __init__(self, extent, spacingX, spacingY, refinement_levels=0, tree=False):

        xmin, xmax, ymin, ymax = extent

        for r in range(0, refinement_levels):
            spacingX = 0.5*spacingX
            spacingY = 0.5*spacingY

        xcoords = np.arange(xmin, xmax+spacingX, spacingX)
        ycoords = np.arange(ymin, ymax+spacingY, spacingY)

        nx, ny = xcoords.size, ycoords.size

        vx = np.ones(nx-2)
        vy = np.ones(ny-2)

        x = np.concatenate([xcoords[1:-1], xcoords[1:-1], vy*xmin, vy*xmax], axis=0)
        y = np.concatenate([vx*ymin, vx*ymax, ycoords[1:-1], ycoords[1:-1]], axis=0)

        print (x.shape, y.shape)

        xy = np.column_stack([x, y])

        # Randomise the point order for triangulation efficiency
        np.random.shuffle(xy)

        # make sure the first points are not collinear
        xy0 = np.array([[xcoords[0] , ycoords[0] ], \
                        [xcoords[-1], ycoords[-1]], \
                        [xcoords[-1], ycoords[0] ], \
                        [xcoords[0] , ycoords[-1]]])

        xy = np.vstack([xy0, xy])

        super(square_border, self).__init__(xy[:,0], xy[:,1], permute=True, tree=tree)

        return


class square_mesh(_cartesian.Triangulation):
    """
    A square mesh where points are uniformly populated
    along x and y directions defined by extent.
    """
    def __init__(self, extent, spacingX, spacingY, random_scale=0.0, refinement_levels=0, tree=False):

        xmin, xmax, ymin, ymax = extent

        xcoords = np.arange(xmin, xmax+spacingX, spacingX)
        ycoords = np.arange(ymin, ymax+spacingY, spacingY)

        x, y = np.meshgrid(xcoords, ycoords)

        interior_mask = np.zeros(x.shape, dtype=bool)
        interior_mask[1:-1,1:-1] = True
        interior_mask = interior_mask.ravel()

        x = x.ravel()
        y = y.ravel()

        nsamples = np.count_nonzero(interior_mask)
        xscale = random_scale*spacingX
        yscale = random_scale*spacingY

        x[interior_mask] += xscale * (0.5 - np.random.rand(nsamples))
        y[interior_mask] += yscale * (0.5 - np.random.rand(nsamples))

        xy = np.column_stack([x, y])
        xy_mask = xy[interior_mask]

        # Randomise the point order for triangulation efficiency
        np.random.shuffle(xy_mask)
        xy[interior_mask] = xy_mask

        # ensure first 3 points are not collinear
        xy[1], xy[-1] = xy[-1].copy(), xy[1].copy()

        super(square_mesh, self).__init__(xy[:,0], xy[:,1], permute=False, tree=tree)

        for r in range(0, refinement_levels):
            X, Y = self.uniformly_refine_triangulation(faces=False, trisect=False)

            # ensure first 3 points are not collinear
            X[1], X[-1] = X[-1].copy(), X[1].copy()
            Y[1], Y[-1] = Y[-1].copy(), Y[1].copy()

            self._update_triangulation(X, Y)

        return


class elliptical_mesh(_cartesian.Triangulation):
    """
    An elliptical mesh where points are successively populated at an
    increasing radius from the midpoint of the extent.

    Caution in parallel and for reproducibility - random noise in point locations !
    """
    def __init__(self, extent, spacingX, spacingY, random_scale=0.0, refinement_levels=0, tree=False):

        xmin, xmax, ymin, ymax = extent

        originX = 0.5*(xmax + xmin)
        originY = 0.5*(ymax + ymin)
        radiusX = 0.5*(xmax - xmin)
        radiusY = 0.5*(ymax - ymin)
        aspect  = 0.5*(ymax - ymin)/radiusX

        spacingXY = np.hypot(spacingX, spacingY)
        radiusXY = np.hypot(radiusX, radiusY)

        radius = np.arange(spacingXY, radiusXY, spacingXY)

        x = []
        y = []
        for r in radius:
            # nsamples must be >= 3
            nsamples = max(2.0*r/spacingXY, 3.0)
            lin_samples = int(nsamples)
            ind = np.arange(0, lin_samples)

            x_ring = originX + np.cos(2.0*np.pi/lin_samples*ind)*r
            y_ring = originY + np.sin(2.0*np.pi/lin_samples*ind)*r * aspect

            x.append(x_ring)
            y.append(y_ring)

        boundary_size = len(x[-1])

        x = np.concatenate(x, axis=0)
        y = np.concatenate(y, axis=0)

        interior_mask = np.ones(x.size, dtype=bool)
        interior_mask[-boundary_size:] = False

        nsamples = interior_mask.sum()
        xscale = random_scale*spacingX
        yscale = random_scale*spacingY

        x[interior_mask] += xscale * (0.5 - np.random.rand(nsamples))
        y[interior_mask] += yscale * (0.5 - np.random.rand(nsamples))

        super(elliptical_mesh, self).__init__(x, y, permute=False, tree=tree)

        for r in range(0, refinement_levels):
            X, Y = self.uniformly_refine_triangulation(faces=True, trisect=False)
            self._update_triangulation(X, Y)

        return


class elliptical_equispaced_mesh(_cartesian.Triangulation):
    """
    An elliptical mesh where points are successively populated at an
    increasing radius from the midpoint of the extent.

    This is a parallel-safe mesh object.
    """
    def __init__(self, axisX, axisY, spacing, refinement_levels=0, tree=False, remove_artifacts=True):

        x, y, mask = elliptical_base_mesh_points(axisX, axisY, spacing)

        super(elliptical_equispaced_mesh, self).__init__(x, y, permute=False, tree=tree)

        for r in range(0, refinement_levels):
            X, Y = self.uniformly_refine_triangulation(faces=False, trisect=False)
            self._update_triangulation(X, Y)

        return


def elliptical_base_mesh_points(axisX, axisY, spacing, remove_artifacts=True):
    """
    Generate well-spaced points in an ellipse - assumes the ellipse is axis-aligned and centred on the origin
    """

    import numpy as np 
    import scipy 
    from scipy import optimize, special

    b = axisX
    a = axisY

    def equal_angles_in_ellipse(arc_length, a, b):
        """ This is a routine that returns equal spaced points around the perimeter of an ellipse
        """
    
        if a == b: 
            tot_size = 2.0 * np.pi * a 
            num = tot_size // arc_length
            angles = 2 * np.pi * np.arange(num) / num
            
            return a * np.cos(angles), a * np.sin(angles)
            
        if (a < b):
            e = (1.0 - a ** 2.0 / b ** 2.0) ** 0.5
        else:
            e = (1.0 - b ** 2.0 / a ** 2.0) ** 0.5       
            
        
        # approximate perimeter of this ellipse    
        h = (a-b)**2 / (a+b)**2
        length = np.pi * (a+b) * ( 1.0 + 3.0 * h / (10.0 + np.sqrt(4.0-3*h)))    
        num = length // arc_length
            
        # This is normalised 
        tot_size = scipy.special.ellipeinc(2.0 * np.pi, e)
        arc_size = tot_size / num
        
        # starting points for search
        angles = 2 * np.pi * np.arange(num) / num
    
        arcs = np.arange(num) * arc_size 
        res = scipy.optimize.root(
            lambda x: (scipy.special.ellipeinc(x, e) - arcs), angles)
        
        angles = res.x 
        
        if a < b: 
            return b * np.sin(angles), a * np.cos(angles)
        else:
            return b * np.cos(angles), a * np.sin(angles)


    pointsx, pointsy = equal_angles_in_ellipse( spacing, a, b)
    bmask = np.full_like(pointsx, 0, dtype=np.bool)
    a -= spacing 
    b -= spacing 

    while (a >= 0.0 and b >= 0.0):
        points = equal_angles_in_ellipse( spacing, a, b)
        pointsx = np.append(pointsx,points[0])
        pointsy = np.append(pointsy,points[1])
        bmask   = np.append(bmask, np.full_like(points[0], 1, dtype=np.bool))
        a -= spacing 
        b -= spacing 


    # The mesh can have some artefacts close to the longer axis so we drop a small fraction of points in that case

    from ._fortran import ntriw
    # from . import _srfpack


    tri = _cartesian.Triangulation(pointsx, pointsy)
    area, weight = ntriw(pointsx, pointsy, tri.simplices.T+1)
    tiny = np.logical_and(bmask, area < np.mean(area)*0.2)

    return pointsx[~tiny], pointsy[~tiny], bmask[~tiny]









class random_mesh(_cartesian.Triangulation):
    """
    A mesh of random points. Take care if you use this is parallel
    as the location of points will not be the same on all processors.


    """
    def __init__(self, extent, number_of_points=5000, tree=False):

        xmin, xmax, ymin, ymax = extent

        deltaX = xmax - xmin
        deltaY = ymax - ymin

        samples = np.sqrt(number_of_points)
        samples_x = int(samples*deltaX/deltaY)
        samples_y = int(samples*deltaY/deltaX)

        spacingX = deltaX/samples_x
        spacingY = deltaY/samples_y

        # boundary nodes
        base_mesh = square_border(extent, spacingX, spacingY)

        xy = np.random.random((number_of_points - base_mesh.npoints,2))

        # scale to extent leaving some buffer space
        x = xmin + 0.5*spacingX + xy[:,0]*(deltaX - 0.5*spacingX)
        y = ymin + 0.5*spacingY + xy[:,1]*(deltaY - 0.5*spacingY)

        x = np.concatenate([base_mesh.x, x], axis=0)
        y = np.concatenate([base_mesh.y, y], axis=0)

        super(random_mesh, self).__init__(x, y, permute=True, tree=tree)

        return

Functions

def elliptical_base_mesh_points(axisX, axisY, spacing, remove_artifacts=True)

Generate well-spaced points in an ellipse - assumes the ellipse is axis-aligned and centred on the origin

Expand source code

def elliptical_base_mesh_points(axisX, axisY, spacing, remove_artifacts=True):
    """
    Generate well-spaced points in an ellipse - assumes the ellipse is axis-aligned and centred on the origin
    """

    import numpy as np 
    import scipy 
    from scipy import optimize, special

    b = axisX
    a = axisY

    def equal_angles_in_ellipse(arc_length, a, b):
        """ This is a routine that returns equal spaced points around the perimeter of an ellipse
        """
    
        if a == b: 
            tot_size = 2.0 * np.pi * a 
            num = tot_size // arc_length
            angles = 2 * np.pi * np.arange(num) / num
            
            return a * np.cos(angles), a * np.sin(angles)
            
        if (a < b):
            e = (1.0 - a ** 2.0 / b ** 2.0) ** 0.5
        else:
            e = (1.0 - b ** 2.0 / a ** 2.0) ** 0.5       
            
        
        # approximate perimeter of this ellipse    
        h = (a-b)**2 / (a+b)**2
        length = np.pi * (a+b) * ( 1.0 + 3.0 * h / (10.0 + np.sqrt(4.0-3*h)))    
        num = length // arc_length
            
        # This is normalised 
        tot_size = scipy.special.ellipeinc(2.0 * np.pi, e)
        arc_size = tot_size / num
        
        # starting points for search
        angles = 2 * np.pi * np.arange(num) / num
    
        arcs = np.arange(num) * arc_size 
        res = scipy.optimize.root(
            lambda x: (scipy.special.ellipeinc(x, e) - arcs), angles)
        
        angles = res.x 
        
        if a < b: 
            return b * np.sin(angles), a * np.cos(angles)
        else:
            return b * np.cos(angles), a * np.sin(angles)


    pointsx, pointsy = equal_angles_in_ellipse( spacing, a, b)
    bmask = np.full_like(pointsx, 0, dtype=np.bool)
    a -= spacing 
    b -= spacing 

    while (a >= 0.0 and b >= 0.0):
        points = equal_angles_in_ellipse( spacing, a, b)
        pointsx = np.append(pointsx,points[0])
        pointsy = np.append(pointsy,points[1])
        bmask   = np.append(bmask, np.full_like(points[0], 1, dtype=np.bool))
        a -= spacing 
        b -= spacing 


    # The mesh can have some artefacts close to the longer axis so we drop a small fraction of points in that case

    from ._fortran import ntriw
    # from . import _srfpack


    tri = _cartesian.Triangulation(pointsx, pointsy)
    area, weight = ntriw(pointsx, pointsy, tri.simplices.T+1)
    tiny = np.logical_and(bmask, area < np.mean(area)*0.2)

    return pointsx[~tiny], pointsy[~tiny], bmask[~tiny]

Classes

class elliptical_equispaced_mesh (axisX, axisY, spacing, refinement_levels=0, tree=False, remove_artifacts=True)

An elliptical mesh where points are successively populated at an increasing radius from the midpoint of the extent.

This is a parallel-safe mesh object.

Expand source code

class elliptical_equispaced_mesh(_cartesian.Triangulation):
    """
    An elliptical mesh where points are successively populated at an
    increasing radius from the midpoint of the extent.

    This is a parallel-safe mesh object.
    """
    def __init__(self, axisX, axisY, spacing, refinement_levels=0, tree=False, remove_artifacts=True):

        x, y, mask = elliptical_base_mesh_points(axisX, axisY, spacing)

        super(elliptical_equispaced_mesh, self).__init__(x, y, permute=False, tree=tree)

        for r in range(0, refinement_levels):
            X, Y = self.uniformly_refine_triangulation(faces=False, trisect=False)
            self._update_triangulation(X, Y)

        return

Ancestors

• Triangulation

Inherited members

• Triangulation:
  • areas
  • centroid_refine_triangulation_by_triangles
  • centroid_refine_triangulation_by_vertices
  • containing_simplex_and_bcc
  • containing_triangle
  • convex_hull
  • edge_lengths
  • edge_refine_triangulation_by_triangles
  • edge_refine_triangulation_by_vertices
  • face_midpoints
  • get_spline_tension_factors
  • gradient
  • gradient_local
  • identify_segments
  • identify_vertex_neighbours
  • identify_vertex_triangles
  • interpolate
  • interpolate_cubic
  • interpolate_linear
  • interpolate_nearest
  • interpolate_to_grid
  • join
  • midpoint_refine_triangulation_by_vertices
  • nearest_vertex
  • nearest_vertices
  • neighbour_and_arc_simplices
  • neighbour_simplices
  • points
  • second_gradient_local
  • segment_midpoints
  • segment_midpoints_by_vertices
  • segment_tripoints
  • simplices
  • smoothing
  • uniformly_refine_triangulation
  • update_tension_factors
  • voronoi_points
  • voronoi_points_and_regions
  • x
  • y

class elliptical_mesh (extent, spacingX, spacingY, random_scale=0.0, refinement_levels=0, tree=False)

An elliptical mesh where points are successively populated at an increasing radius from the midpoint of the extent.

Caution in parallel and for reproducibility - random noise in point locations !

Expand source code

class elliptical_mesh(_cartesian.Triangulation):
    """
    An elliptical mesh where points are successively populated at an
    increasing radius from the midpoint of the extent.

    Caution in parallel and for reproducibility - random noise in point locations !
    """
    def __init__(self, extent, spacingX, spacingY, random_scale=0.0, refinement_levels=0, tree=False):

        xmin, xmax, ymin, ymax = extent

        originX = 0.5*(xmax + xmin)
        originY = 0.5*(ymax + ymin)
        radiusX = 0.5*(xmax - xmin)
        radiusY = 0.5*(ymax - ymin)
        aspect  = 0.5*(ymax - ymin)/radiusX

        spacingXY = np.hypot(spacingX, spacingY)
        radiusXY = np.hypot(radiusX, radiusY)

        radius = np.arange(spacingXY, radiusXY, spacingXY)

        x = []
        y = []
        for r in radius:
            # nsamples must be >= 3
            nsamples = max(2.0*r/spacingXY, 3.0)
            lin_samples = int(nsamples)
            ind = np.arange(0, lin_samples)

            x_ring = originX + np.cos(2.0*np.pi/lin_samples*ind)*r
            y_ring = originY + np.sin(2.0*np.pi/lin_samples*ind)*r * aspect

            x.append(x_ring)
            y.append(y_ring)

        boundary_size = len(x[-1])

        x = np.concatenate(x, axis=0)
        y = np.concatenate(y, axis=0)

        interior_mask = np.ones(x.size, dtype=bool)
        interior_mask[-boundary_size:] = False

        nsamples = interior_mask.sum()
        xscale = random_scale*spacingX
        yscale = random_scale*spacingY

        x[interior_mask] += xscale * (0.5 - np.random.rand(nsamples))
        y[interior_mask] += yscale * (0.5 - np.random.rand(nsamples))

        super(elliptical_mesh, self).__init__(x, y, permute=False, tree=tree)

        for r in range(0, refinement_levels):
            X, Y = self.uniformly_refine_triangulation(faces=True, trisect=False)
            self._update_triangulation(X, Y)

        return

Ancestors

• Triangulation

Inherited members

• Triangulation:
  • areas
  • centroid_refine_triangulation_by_triangles
  • centroid_refine_triangulation_by_vertices
  • containing_simplex_and_bcc
  • containing_triangle
  • convex_hull
  • edge_lengths
  • edge_refine_triangulation_by_triangles
  • edge_refine_triangulation_by_vertices
  • face_midpoints
  • get_spline_tension_factors
  • gradient
  • gradient_local
  • identify_segments
  • identify_vertex_neighbours
  • identify_vertex_triangles
  • interpolate
  • interpolate_cubic
  • interpolate_linear
  • interpolate_nearest
  • interpolate_to_grid
  • join
  • midpoint_refine_triangulation_by_vertices
  • nearest_vertex
  • nearest_vertices
  • neighbour_and_arc_simplices
  • neighbour_simplices
  • points
  • second_gradient_local
  • segment_midpoints
  • segment_midpoints_by_vertices
  • segment_tripoints
  • simplices
  • smoothing
  • uniformly_refine_triangulation
  • update_tension_factors
  • voronoi_points
  • voronoi_points_and_regions
  • x
  • y

class random_mesh (extent, number_of_points=5000, tree=False)

A mesh of random points. Take care if you use this is parallel as the location of points will not be the same on all processors.

Expand source code

class random_mesh(_cartesian.Triangulation):
    """
    A mesh of random points. Take care if you use this is parallel
    as the location of points will not be the same on all processors.


    """
    def __init__(self, extent, number_of_points=5000, tree=False):

        xmin, xmax, ymin, ymax = extent

        deltaX = xmax - xmin
        deltaY = ymax - ymin

        samples = np.sqrt(number_of_points)
        samples_x = int(samples*deltaX/deltaY)
        samples_y = int(samples*deltaY/deltaX)

        spacingX = deltaX/samples_x
        spacingY = deltaY/samples_y

        # boundary nodes
        base_mesh = square_border(extent, spacingX, spacingY)

        xy = np.random.random((number_of_points - base_mesh.npoints,2))

        # scale to extent leaving some buffer space
        x = xmin + 0.5*spacingX + xy[:,0]*(deltaX - 0.5*spacingX)
        y = ymin + 0.5*spacingY + xy[:,1]*(deltaY - 0.5*spacingY)

        x = np.concatenate([base_mesh.x, x], axis=0)
        y = np.concatenate([base_mesh.y, y], axis=0)

        super(random_mesh, self).__init__(x, y, permute=True, tree=tree)

        return

Ancestors

• Triangulation

Inherited members

• Triangulation:
  • areas
  • centroid_refine_triangulation_by_triangles
  • centroid_refine_triangulation_by_vertices
  • containing_simplex_and_bcc
  • containing_triangle
  • convex_hull
  • edge_lengths
  • edge_refine_triangulation_by_triangles
  • edge_refine_triangulation_by_vertices
  • face_midpoints
  • get_spline_tension_factors
  • gradient
  • gradient_local
  • identify_segments
  • identify_vertex_neighbours
  • identify_vertex_triangles
  • interpolate
  • interpolate_cubic
  • interpolate_linear
  • interpolate_nearest
  • interpolate_to_grid
  • join
  • midpoint_refine_triangulation_by_vertices
  • nearest_vertex
  • nearest_vertices
  • neighbour_and_arc_simplices
  • neighbour_simplices
  • points
  • second_gradient_local
  • segment_midpoints
  • segment_midpoints_by_vertices
  • segment_tripoints
  • simplices
  • smoothing
  • uniformly_refine_triangulation
  • update_tension_factors
  • voronoi_points
  • voronoi_points_and_regions
  • x
  • y

class square_border (extent, spacingX, spacingY, refinement_levels=0, tree=False)

Square border to add to any mesh. Creates a set of points around the extent of the domain.

Expand source code

class square_border(_cartesian.Triangulation):
    """
    Square border to add to any mesh.
    Creates a set of points around the extent of the domain.
    """
    def __init__(self, extent, spacingX, spacingY, refinement_levels=0, tree=False):

        xmin, xmax, ymin, ymax = extent

        for r in range(0, refinement_levels):
            spacingX = 0.5*spacingX
            spacingY = 0.5*spacingY

        xcoords = np.arange(xmin, xmax+spacingX, spacingX)
        ycoords = np.arange(ymin, ymax+spacingY, spacingY)

        nx, ny = xcoords.size, ycoords.size

        vx = np.ones(nx-2)
        vy = np.ones(ny-2)

        x = np.concatenate([xcoords[1:-1], xcoords[1:-1], vy*xmin, vy*xmax], axis=0)
        y = np.concatenate([vx*ymin, vx*ymax, ycoords[1:-1], ycoords[1:-1]], axis=0)

        print (x.shape, y.shape)

        xy = np.column_stack([x, y])

        # Randomise the point order for triangulation efficiency
        np.random.shuffle(xy)

        # make sure the first points are not collinear
        xy0 = np.array([[xcoords[0] , ycoords[0] ], \
                        [xcoords[-1], ycoords[-1]], \
                        [xcoords[-1], ycoords[0] ], \
                        [xcoords[0] , ycoords[-1]]])

        xy = np.vstack([xy0, xy])

        super(square_border, self).__init__(xy[:,0], xy[:,1], permute=True, tree=tree)

        return

Ancestors

• Triangulation

Inherited members

• Triangulation:
  • areas
  • centroid_refine_triangulation_by_triangles
  • centroid_refine_triangulation_by_vertices
  • containing_simplex_and_bcc
  • containing_triangle
  • convex_hull
  • edge_lengths
  • edge_refine_triangulation_by_triangles
  • edge_refine_triangulation_by_vertices
  • face_midpoints
  • get_spline_tension_factors
  • gradient
  • gradient_local
  • identify_segments
  • identify_vertex_neighbours
  • identify_vertex_triangles
  • interpolate
  • interpolate_cubic
  • interpolate_linear
  • interpolate_nearest
  • interpolate_to_grid
  • join
  • midpoint_refine_triangulation_by_vertices
  • nearest_vertex
  • nearest_vertices
  • neighbour_and_arc_simplices
  • neighbour_simplices
  • points
  • second_gradient_local
  • segment_midpoints
  • segment_midpoints_by_vertices
  • segment_tripoints
  • simplices
  • smoothing
  • uniformly_refine_triangulation
  • update_tension_factors
  • voronoi_points
  • voronoi_points_and_regions
  • x
  • y

class square_mesh (extent, spacingX, spacingY, random_scale=0.0, refinement_levels=0, tree=False)

A square mesh where points are uniformly populated along x and y directions defined by extent.

Expand source code

class square_mesh(_cartesian.Triangulation):
    """
    A square mesh where points are uniformly populated
    along x and y directions defined by extent.
    """
    def __init__(self, extent, spacingX, spacingY, random_scale=0.0, refinement_levels=0, tree=False):

        xmin, xmax, ymin, ymax = extent

        xcoords = np.arange(xmin, xmax+spacingX, spacingX)
        ycoords = np.arange(ymin, ymax+spacingY, spacingY)

        x, y = np.meshgrid(xcoords, ycoords)

        interior_mask = np.zeros(x.shape, dtype=bool)
        interior_mask[1:-1,1:-1] = True
        interior_mask = interior_mask.ravel()

        x = x.ravel()
        y = y.ravel()

        nsamples = np.count_nonzero(interior_mask)
        xscale = random_scale*spacingX
        yscale = random_scale*spacingY

        x[interior_mask] += xscale * (0.5 - np.random.rand(nsamples))
        y[interior_mask] += yscale * (0.5 - np.random.rand(nsamples))

        xy = np.column_stack([x, y])
        xy_mask = xy[interior_mask]

        # Randomise the point order for triangulation efficiency
        np.random.shuffle(xy_mask)
        xy[interior_mask] = xy_mask

        # ensure first 3 points are not collinear
        xy[1], xy[-1] = xy[-1].copy(), xy[1].copy()

        super(square_mesh, self).__init__(xy[:,0], xy[:,1], permute=False, tree=tree)

        for r in range(0, refinement_levels):
            X, Y = self.uniformly_refine_triangulation(faces=False, trisect=False)

            # ensure first 3 points are not collinear
            X[1], X[-1] = X[-1].copy(), X[1].copy()
            Y[1], Y[-1] = Y[-1].copy(), Y[1].copy()

            self._update_triangulation(X, Y)

        return

Ancestors

• Triangulation

Inherited members

• Triangulation:
  • areas
  • centroid_refine_triangulation_by_triangles
  • centroid_refine_triangulation_by_vertices
  • containing_simplex_and_bcc
  • containing_triangle
  • convex_hull
  • edge_lengths
  • edge_refine_triangulation_by_triangles
  • edge_refine_triangulation_by_vertices
  • face_midpoints
  • get_spline_tension_factors
  • gradient
  • gradient_local
  • identify_segments
  • identify_vertex_neighbours
  • identify_vertex_triangles
  • interpolate
  • interpolate_cubic
  • interpolate_linear
  • interpolate_nearest
  • interpolate_to_grid
  • join
  • midpoint_refine_triangulation_by_vertices
  • nearest_vertex
  • nearest_vertices
  • neighbour_and_arc_simplices
  • neighbour_simplices
  • points
  • second_gradient_local
  • segment_midpoints
  • segment_midpoints_by_vertices
  • segment_tripoints
  • simplices
  • smoothing
  • uniformly_refine_triangulation
  • update_tension_factors
  • voronoi_points
  • voronoi_points_and_regions
  • x
  • y